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It is not necessarily true that the convolution of an infinite-length sequence with a finite-length sequence will be infinite in length. It may be either. Clearly, if x ( n ) = 6 ( n ) and h ( n ) = (OS)"u(n), the convolution will be an infinite-length sequence. However, it is possible for the finite-length sequence to remove the infinite-length tail of an infinite-length sequence. For example, note that

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Forming the sum of the products x(k)h(-k), we obtain the value of y ( n ) at time n = 0 , which is y ( 0 ) = 2 . Shifting h(-k) to the left by one, multiplying and adding, we obtain the value of y ( n ) at n = -1, which is y ( - I ) = 2. Shifting one more time to the left, forming the sum of products, we find y ( - 2 ) = 1, which is the last nonzero value of y ( n ) for n < 0 . Repeating the process by shifting h ( - k ) to the right, we obtain the values of y ( n ) for n > 0 , which are